At the first step, the low dimensional feature maps \(\lbrace {\bf G}^t\rbrace _{t \in {\bf T}}\)  are generated by PCA [1]} projection, \({\bf G} = \phi _{PCA}({\bf F})\) , where \({\bf G} \in \mathbb {R}^{W_x \times W_y \times d}, {\bf F} \in \mathbb {R}^{W_x \times W_y \times D}\)  and \(d \ll D\) . Then, the epitome of \(\lbrace {\bf G}^t\rbrace _{t \in {\bf T}}\)  can be learned with
\(\begin{aligned}{\rm {E}} \ {\rm {step:}}\ \ & \hat{q}(l^t={\bf {k}}) \propto \prod _{{\bf {i}}\in {\bf {W}}_{\bf k}}\mathcal {N}\left({g}^{t}_{\bf i-k};\hat{\mu }_{\bf i},\hat{\sigma }^2_{\bf i}\right), \\{\rm {M}} \ {\rm {step:}}\ \ & \hat{\mu }_{\bf i} = \frac{\sum _{t \in {\bf T}}{\sum _{\bf k \in W_{i-W}}{\hat{q}(l^t={\bf {k}})}{g}^t_{\bf i-k}}}{\sum _{t \in {\bf T}}{\sum _{\bf k \in W_{i-W}}{\hat{q}(l^t={\bf {k}})}}}, \\& \hat{\sigma }^2_{\bf i} = \frac{\sum _{t \in {\bf T}}{\sum _{\bf k \in W_{i-W}}{\hat{q}(l^t={\bf {k}})}({g}^t_{\bf i-k}-\hat{\mu }_{\bf i})^2}}{\sum _{t \in {\bf T}}{\sum _{\bf k \in W_{i-W}}{\hat{q}(l^t={\bf {k}})}}}.\end{aligned}\) 
